Accusing the WHO of giving bad advice, being “China-centric” and even withholding information, Trump claimed to have stopped US funding in a press briefing on Tuesday, only to claim a few minutes later that he was just considering it, pending a review of its performance.

In fact, the US is already about $200m in arrears in assessed contributions (national membership fees). It has given more in donations, and was the biggest single donor in 2019 – certainly far more than China, which gives a paltry amount given the size of its economy.

But the US is far from providing the majority of the WHO’s funds, as Trump claimed, and its voluntary contributions have largely been tied to specific projects. WHO’s total annual budget is about $2.5bn, and contributions from member states have not significantly increased over three decades.

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Donald Trump blames WHO for dire situation in the US, threatens to pull funding – video

“The WHO’s budget is around the equivalent of a large US hospital, which is utterly incommensurate with its global responsibilities,” said Lawrence Gostin, a public health law professor at Georgetown University. “So, if the US president were a global health leader, he’d be leading a call to at minimum double the WHO budget in the face of this pandemic.”

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Global health experts have generally given the WHO good marks for its transparency and the speed with which it has responded to the coronavirus, under its director general, Tedros Adhanom Ghebreyesus. It is universally seen as much better than its sluggish, error-strewn response to the Ebola outbreak in west Africa in 2014, three years before Tedros took over.

“I have been a longstanding critic and I’ve described their performance on Ebola as catastrophic. But I think overall their performance on this outbreak has been, not perfect, but pretty good,” Ashish Jha, a public health professor at Harvard, said.

“They’ve been very transparent as much as they have known the data. They have had daily calls, they have been very clear about the severity of this illness, and how the global community has to respond.”

Anthony Fauci, the director of the US National Institute of Allergy and Infectious Diseases, and Robert Redfield, the head of the Centers for Disease Control and Prevention, took part in WHO conference calls about coronavirus from 7 January, according to sources familiar with the conversations.

Donald Trump rails against the WHO at a White House coronavirus briefing on 5 April. Photograph: Tasos Katopodis/EPA

On the same day Trump was confidently predicting the coronavirus did not present a serious threat to the US, assuring Americans: “It’s going to have a very good ending.”

Gavin Yamey, the director of Duke University’s center for policy impact in global health, said: “If the United States had followed the WHO’s very clear advice on identifying cases, isolating cases and conducting contact tracing, then it wouldn’t be in the appalling situation that it is in today.”

Despite its declaration, the WHO did not advocate travel restrictions of the sort imposed by Trump a day later on non-American travellers arriving from China. The president has pointed to this as an example of bad advice. But Gostin, who is director of the WHO centre on global health law, said that the organisation cannot generally call for travel bans under international law – and such bans can be counterproductive, leading countries to withhold vital information for fear of economic isolation.

“To blame the WHO for acting on the basis of international law and science in ways that are entirely consistent with what WHO practices have been for decades is the height of hypocrisy,” he said.

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Trump claimed that his ban “shut down” intercontinental transmission of the virus, but an ABC television investigation found that there were 3,200 flights from China to the US in the critical period between December and March.

By the time Trump’s ban was announced, it was far too late to stop the virus entering the US. It was already rampant in US communities, but Trump continued to tell Americans that the outbreak would not affect them, and wholesale US testing failed to get off the ground for another six weeks.

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The US president’s accusations that the WHO is “China-centric” have more resonance with public health scholars. The WHO has largely excluded Taiwan from its discussions, and dodged questions about the Taiwanese response, which has been one of the most effective. But because of pressure from Beijing – which sees Taiwan as an integral part of its territory and opposes any form of recognition – the blindspot is a UN-wide phenomenon.

Tedros also praised Chinese transparency and its national response, lauding President Xi Jinping for his “political leadership”, even though Beijing had tried to hide the seriousness of the situation in Wuhan for several critical weeks,.

Tedros Adhanom Ghebreyesus, the director general of the WHO, attends a meeting with the Chinese president, Xi Jinping in Beijing on 28 January 2020. Photograph: Naohiko Hatta/Pool/EPA

“I think the effusive praise for China, in the early days, was probably unnecessary,” Jha said.

Other say that a certain amount of diplomatic flattery was necessary to coax Xi into allowing in WHO experts and sharing information.

Amanda Glassman, the executive vice-president and senior fellow at the Center for Global Development, said a deeper problem is the WHO’s low budget and relatively toothless structure. Unlike the nuclear watchdog, the International Atomic Energy Agency, it has no redress against governments that do not cooperate.

“It operates in countries at the pleasure and permission of the host country governments. So in the case of China, to be allowed to enter China, it was a negotiation to get there,” Glassman said.

She added that the real challenge for the WHO has yet come, when the pandemic really hits poorer countries with fragile, underfunded health services, who rely heavily on the organisation.

Unlike the Ebola outbreak in 2014, the US will not be there to take the lead, and it will be up to the WHO to coordinate scarce resources and expertise.

“Can they do that in 40 countries at once?” Glassman asked. “That is the part that remains to be tested.”